Cone Volume Calculator
Calculate the volume of a cone by entering its radius and height. A cone is a 3D shape with a circular base and a single vertex.
Formula:
Volume=13× π × r² × h
Where:
- π = Pi (approximately 3.14159)
- r = Radius of the base
- h = Height of the cone
Unit of Measurement:
cm
The radius of the cone base
cm
The height of the cone
Result
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About Cone Volume
A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex.
The volume of a cone is one-third of the volume of a cylinder with the same base and height. The formula is V = (1/3) × π × r² × h, where r is the radius of the base and h is the height of the cone.
For example, if the radius is 3 cm and the height is 6 cm, the volume would be (1/3) × π × 3² × 6 = (1/3) × π × 9 × 6 ≈ 56.5 cm³.
How to Calculate Cone Volume
Step 1: Measure the Radius
Measure the radius of the circular base of the cone. The radius is the distance from the center of the circle to any point on its edge. If you have the diameter (d) instead, remember that radius = diameter ÷ 2.
Step 2: Measure the Height
Measure the height of the cone, which is the perpendicular distance from the center of the base to the apex (tip) of the cone. Make sure to measure from the center of the base, not from the edge.
Step 3: Apply the Formula
Use the formula V = (1/3) × π × r² × h. First calculate r² (radius squared), then multiply by π, then by the height, and finally by 1/3. For example, if r = 3 cm and h = 6 cm: V = (1/3) × π × 3² × 6 = (1/3) × π × 9 × 6 ≈ 56.5 cm³.
Practical Applications
Construction
Engineers use cone volume calculations for designing conical roofs, silos, and funnels.
Manufacturing
Cone volumes are essential for producing conical containers, packaging, and components.
Food Industry
Used to calculate volumes of ice cream cones, conical filters, and dispensers.
Education
Cone volume formulas are fundamental in teaching 3D geometry and calculus concepts.
Tips and Common Mistakes
- Confusing Slant Height: The height of a cone is the perpendicular distance from the base to the apex, not the slant height along the side.
- Diameter vs. Radius: Make sure you're using the radius in your calculations, not the diameter (radius = diameter ÷ 2).
- Forgetting the 1/3: The most common mistake is forgetting to multiply by 1/3 in the formula. A cone's volume is one-third of a cylinder with the same base and height.
- Unit Consistency: Ensure all measurements (radius and height) use the same unit before calculating.
Frequently Asked Questions
The height of a cone is the perpendicular distance from the center of the base to the apex (tip) of the cone. The slant height is the distance from the edge of the base to the apex, measured along the surface of the cone. In volume calculations, you must use the height (perpendicular distance), not the slant height. Think of the height as the altitude of the cone.
Related Calculators
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.
Need Help?
Check out our guide on how to use this calculator properly and understand the concepts behind it.
Learn how to calculate volume